Discrete energy transport in the perturbed Ablowitz-Ladik equation for Davydov model of α-helix proteins

The modulational instability of a plane wave for the perturbed non-integrable Ablowitz-Ladik equation for α-helix proteins is analyzed. Through the linear stability analysis, we observe that the presence of additional terms in the Ablowitz-Ladik equation tends to suppress modulational instability. Numerical simulations are performed in order to verify our analytical predictions. The presence of extended terms in the Ablowitz-Ladik equation tends to compactify and split the emerging localized structures. Particular attention is paid to the emergence of multi-hump structures, and the biological relevance of the latter is discussed. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012